DE102022208614A1 - Reconstruction of training examples in federated training of neural networks - Google Patents

Abstract

Method (100) for reconstructing training examples x, with which a given neural network (1) was trained to optimize a given cost function L, with the steps: • A quality function R is provided (110), which is for a reconstructed Training example x̃ measures the extent to which it belongs to an expected domain or distribution of the training examples x; • a size B of a batch of training examples x with which the neural network 1 was trained is provided (120); • a The gradient dL/dMW of the cost function L determined during this training according to parameters MW that characterize the behavior of the neural network (1) is divided into a partition of B components Pj (130); Dependence of the outputs yivof neurons in the input layer of the neural network (1), which receives the training examples x, on the parameters MW,i of these neurons and the training examples x a training examplex˜jTreconstructed (140);• the ones obtained in this way Reconstructions x˜jT are evaluated with the quality function R (150); R is improved.

Description

The present invention relates to federated training of neural networks, in which multiple clients contribute to the training based on local inventories of training examples.

State of the art

To train neural networks that can be used, for example, as classifiers for images or other measurement data, a large number of training examples with sufficient variability are required. If the training examples contain personal data, such as images of faces or license plates, collecting training examples from a large number of countries, each with different data protection regulations, becomes legally problematic. In addition, images or video data, for example, have a very large volume, so the centralized collection requires a lot of bandwidth and storage space.

Therefore, in federated learning, the neural network is issued by a central entity to many clients, each of which then trains the network with their local assets and determines suggestions for changes to the network's parameters. These suggestions are aggregated by the central entity into a final update of the parameters.

In this way, only parameters of the neural network and its changes are exchanged between the central entity and the clients.

The other side of this coin is that some control over the quality of the ultimate training success is given away.

Disclosure of the invention

The invention provides a method for reconstructing training examples x with which a given neural network was trained to optimize a given cost function L. The cost function L is known to all participants, especially in federated training.

As part of the process, a quality function R is first provided. Regardless of how a reconstructed training example x̃ was obtained, this quality function R for this reconstructed training example x̃ measures the extent to which it belongs to an expected domain or distribution of the training examples. The quality function R therefore outputs a score that indicates how well the reconstructed training example x̃ fits into the expected domain or distribution. This means that the goal is that the reconstructed training example x̃ fits there and is open to optimization, true to Archimedes' maxim that any load can be moved if there is only one starting point for a lever.

A size B of a batch of training examples x with which the neural network was trained is also provided. In federated training, which is carried out by a plurality of decentralized clients C and coordinated by a central entity Q, B is usually either specified by the central entity Q or communicated to the central entity Q by the clients C. If B is not known, an estimate can be used as a substitute and the refinement of this estimate can be included in the optimization described below.

als Summe ausgeführt sein.The size B is used to divide a gradient dL/dM _W of the cost function L determined during training into a partition of B components P _j according to parameters M _W that characterize the behavior of the neural network. In federated learning, the gradient dL/dM _W is typically what is reported back by clients C to a coordinating central entity Q. For example, the partition can be according to $${\displaystyle \sum _{j=\mathrm{1,}\dots ,b}\frac{1}{b}{P}_j=\frac{dL}{d{M}_W}}$$

be executed as a sum.

rekonstruiert. Wie im Folgenden näher erläutert werden wird, ist eine solche Rekonstruktion unter der vereinfachenden Annahme, dass ein einzelnes Trainings-Beispiel x mindestens ein Neuron in der Eingangsschicht aktiviert, möglich.Each component P _j of the gradient dL/dM _W is calculated using the functional dependence of the outputs y _i of neurons in the input layer of the neural network, which receives the training examples x, on the parameters M _W,i of these neurons and the trainings -Examples x a training example ${\tilde{x}}_j^T$

reconstructed. As will be explained in more detail below, such a reconstruction is possible under the simplifying assumption that a single training example x activates at least one neuron in the input layer.

Such a reconstruction requires that the gradient dL/dM _W of the cost function L based on this training example x is known. With federated learning, however, a gradient dL/dM _W is typically reported back, which is aggregated across all B training examples in the batch, so that no direct conclusion can be drawn about a single training example. The one suggested here The method therefore carries out the reconstruction separately for each component P _j of the gradient dL/dM _W and hereby reduces the problem to the task of finding the correct partition of the gradient dL/dM _W in components P _j .

werden mit der Gütefunktion R bewertet. Die Partition in die Komponenten P_j wird dann auf das Ziel optimiert, dass bei erneuter Aufteilung des Gradienten der Kostenfunktion und Rekonstruktion neuer Trainings-Beispiele ${\tilde{x}}_j^T$

deren Bewertung durch die Gütefunktion R verbessert wird.For this purpose, the reconstructions obtained for all components P _j are used ${\tilde{x}}_j^T$

are evaluated with the quality function R. The partition into the components P _j is then optimized to the goal of splitting the gradient of the cost function again and reconstructing new training examples ${\tilde{x}}_j^T$

whose evaluation is improved by the quality function R.

eines Trainings-Beispiels erzeugt wird, auf solche Rekonstruktionen ${\tilde{x}}_j^T$

führt, die der erwarteten Domäne oder Verteilung der Trainings-Beispiele angehören. Somit ist lediglich Vorwissen in Bezug auf diese erwartete Domäne oder Verteilung nötig, um jedes einzelne Trainings-Beispiel x₁, ...,x_B zumindest näherungsweise zu rekonstruieren.Ultimately, in the space of possible partitions of the gradient dL/dM _W in components P _j , a search is made for the partition which, if a reconstruction is possible for each component P _j according to this partition ${\tilde{x}}_j^T$

of a training example is generated on such reconstructions ${\tilde{x}}_j^T$

leads that belong to the expected domain or distribution of the training examples. Thus, only prior knowledge regarding this expected domain or distribution is required to at least approximately reconstruct each individual training example x ₁ , ...,x _B.

Even an approximate reconstruction that is not of the best quality already provides valuable information about the quality of the training. In particular, it can be checked, for example, whether the correct type of training examples x was used as specified by the central coordinating entity Q. For example, if a neural network is trained for a driving assistance system or for an at least partially automated motor vehicle that classifies or otherwise processes images of traffic situations, training examples of traffic situations that were recorded from the perspective of a motor vehicle are required. For example, one of the clients could misunderstand the instructions for collecting training examples and use training examples recorded with a cyclist's helmet camera. Introducing these training examples could make the performance of the neural network ultimately intended for automobiles worse instead of better. Such errors can be discovered through even an imperfect reconstruction.

• • Klassifikations-Scores in Bezug auf eine oder mehrere Klassen einer vorgegebenen Klassifikation, und/oder
• • eine semantische Segmentierung dahingehend, dass jedes Pixel einer Klasse zugeordnet wird, und/oder
• • in dem Eingabe-Bild enthaltene Instanzen von Objekten

auszuwerten.Images as training examples x are also a preferred use case in other respects. They have a high volume compared to other types of data, so federated learning saves a lot of storage space and bandwidth for data transfer. Images are also particularly sensitive in terms of data protection. Thus, in a particularly advantageous embodiment, a neural network is selected which is designed to generate an input image divided into pixels or composed of pixels on the basis of the pixel values

• • Classification scores related to one or more classes of a given classification, and/or
• • a semantic segmentation such that each pixel is assigned to a class, and/or
• • Instances of objects contained in the input image

to evaluate.

In a particularly advantageous embodiment, shares p _j · dL/dM _W with weights p _j and Σ _j p _j = 1 are selected as components P _j of the partition. For the values of the weights p _j then 0 < p _j < 1 applies, which is advantageous for numerical optimization.

In a further advantageous embodiment, a gradient of the quality function R is propagated back to changes in the weights p _j . The proven gradient-based methods can then be used to find the optimum, such as a stochastic gradient descent method.

The weights p _j can in particular be initialized, for example, with softmax values formed from logits of the neural network. These logits are raw outputs of a layer of the neural network and thus provide an initial indication of which of the training examples x in the batch contributed particularly strongly to the gradient dL/dM _W.

und Bias-Werte b_i als Parameter M_W,i umfasst. In einem solchen Netzwerk

• • multipliziert ein i-tes Neuron ein diesem Neuron zugeführtes Trainingsbeispiel x mit Gewichten $w_i^T,$
  
• • addiert das Neuron zu dem Ergebnis einen Bias-Wert b_i, um so einen Aktivierungswert des Neurons zu erhalten und
• • ermittelt das Neuron eine Ausgabe y_i durch Anwenden einer nichtlinearen Aktivierungsfunktion auf diesen Aktivierungswert.

In a particularly advantageous embodiment, a neural network is selected that weights $w_i^T$

and bias values b _i as parameters M _W,i . In such a network

• • an i-th neuron multiplies a training example x fed to this neuron by weights $w_i^T,$
  
• • the neuron adds a bias value b _i to the result in order to obtain an activation value of the neuron and
• • the neuron determines an output y _i by applying a nonlinear activation function to this activation value.

The activation value is then a linear function of the training example x. The activation function can in particular, for example, be designed so that it is linear at least in sections. For example, the “Rectified Linear Unit (ReLU)” function passes the positive portion of its argument through unchanged.

so dass für Ausgaben y_i > 0 abgeleitet werden kann: $$\frac{dL}{d{b}_i}=\frac{dL}{d{y}_i}\frac{d{y}_i}{d{b}_i}=\frac{dL}{d{y}_i}$$

wegen dy_i/db_i = 1. Analog gilt $$\frac{dL}{d{w}_i^T}=\frac{dL}{d{y}_i}\frac{d{y}_i}{d{w}_i^T}=\frac{dL}{d{b}_i}{x}^T.$$

If in the neural network the input layer of the neural network is immediately followed by a dense layer whose neurons are connected to all neurons of the input layer, the output y _i of the ith neuron is given by $$y_i=\text{ReLU}\left(w_i^{T}x+b_i\right),$$

so that for outputs y _i > 0 it can be derived: $$\frac{dL}{d{b}_i}=\frac{dL}{d{y}_i}\frac{d{y}_i}{d{b}_i}=\frac{dL}{d{y}_i}$$

because dy _i /db _i = 1. The same applies $$\frac{dL}{d{w}_i^T}=\frac{dL}{d{y}_i}\frac{d{y}_i}{d{w}_i^T}=\frac{dL}{d{b}_i}{x}^T.$$

unter der ebenfalls vom neuronalen Netzwerk zu erfüllenden Voraussetzung, dass (dL/db_i) ≠ 0.The reconstruction x̃ ^T of the training example x ^T can therefore be calculated as $${\tilde{x}}^T={\left(\frac{dL}{d{b}_i}\right)}^{-1}\left(\frac{dL}{d{w}_i^T}\right)$$

under the condition, which also has to be fulfilled by the neural network, that (dL/db _i ) ≠ 0.

zu erhalten. Es werden also aus der Komponente P_j des Gradienten dL/dM_W Gradienten dL/db_i der Kostenfunktion L nach dem Bias b_i und Gradienten $dL/d{w}_i^T$

der Kostenfunktion L nach den Gewichten $w_i^T$

ermittelt, und aus diesen Gradienten dL/db_i und $dL/d{w}_i^T$

wird die gesuchte Rekonstruktion ${\tilde{x}}_j^T$

des Trainings-Beispiels ermittelt. Mit fortschreitender Optimierung der Partition des Gradienten dL/dM_W in die Komponenten P_j werden auch die Rekonstruktionen ${\tilde{x}}_j^T$

immer besser.As explained previously, this calculation is carried out separately for each component P _j of the gradient dL/dM _W , in each case a reconstruction ${\tilde{x}}_j^T$

to obtain. The component P _j of the gradient dL/dM _W thus becomes gradients dL/db _i of the cost function L according to the bias b _i and gradients $dL/d{w}_i^T$

the cost function L according to the weights $w_i^T$

determined, and from these gradients dL/db _i and $dL/d{w}_i^T$

becomes the reconstruction you are looking for ${\tilde{x}}_j^T$

of the training example. As the partition of the gradient dL/dM _W into the components P _j progresses, so do the reconstructions ${\tilde{x}}_j^T$

better and better.

In a particularly advantageous embodiment, a trained discriminator of a Generative Adversarial Network, GAN, is selected as the quality function R. Such a discriminator has learned to distinguish real samples from the expected domain or distribution from samples generated with a GAN generator. For example, a classification score output by the discriminator can be used as the value of the quality function R. Probabilistic models can also be used, for example, which make it possible to estimate density distributions of the training examples x using likelihood functions (such as the Bayesian models also used for spam filtering of emails).

sind nicht ganz so detailreich und somit für Unbefugte schlechter ausnutzbar.The training examples x can in particular represent, for example, images and/or time series of measured values. Images in particular are particularly large in volume and sensitive in terms of data protection, making federated training particularly advantageous. Detailed time series of measured values in industrial plants can also allow conclusions to be drawn about the internals of a production process that are not intended for the public. The reconstructed training examples ${\tilde{x}}_j^T$

are not quite as detailed and therefore harder to exploit for unauthorized persons.

dem neuronalen Netzwerk als Validierungsdaten zugeführt. Die daraufhin vom neuronalen Netzwerk gelieferten Ausgaben mit Soll-Ausgaben verglichen, mit denen diese rekonstruierten Trainings-Beispiele (aus beliebiger Quelle) gelabelt sind. Anhand des Ergebnisses dieses Vergleichs wird ermittelt, inwieweit das neuronale Netzwerk hinreichend auf ungesehene Daten generalisiert. Die rekonstruierten Trainings-Beispiele ${\tilde{x}}_j^T$

sind insofern optimale Testobjekte, als sie ausweislich der Gütefunktion R erwiesenermaßen der Domäne oder Verteilung der ursprünglichen Trainings-Beispiele x angehören, ohne mit irgendeinem dieser Trainings-Beispiele x identisch zu sein.In a particularly advantageous embodiment, the reconstructed training examples ${\tilde{x}}_j^T$

fed to the neural network as validation data. The outputs then provided by the neural network are compared with target outputs with which these reconstructed training examples (from any source) are labeled. The result of this comparison is used to determine the extent to which the neural network generalizes sufficiently to unseen data. The reconstructed training examples ${\tilde{x}}_j^T$

are optimal test objects in that, according to the quality function R, they belong to the domain or distribution of the original training examples x without being identical to any of these training examples x.

If this test shows that the neural network generalizes sufficiently to unseen data, the network can be used in its intended operational mode. The neural network is then advantageously supplied with measurement data that was recorded with at least one sensor. A control signal is determined from the output then provided by the neural network. A vehicle, a driving assistance system, a quality control system, an area monitoring system, and/or a medical imaging system is controlled with the control signal. In this context, the reconstruction of training examples using the method proposed here ultimately offers an increased degree of certainty that the reaction carried out by the controlled system to the control signal is appropriate to the situation represented by the measurement data.

As explained above, within the framework of federated training, the reconstruction is advantageously carried out by a central entity Q, which distributes the neural network to a plurality of clients C for the purpose of federated training. The gradient dL/dM _W of the cost function L according to the parameters M _W is determined by a client C when training the neural network on a batch with B training examples x and aggregated over these B training examples x. As explained previously, this makes it possible to check whether the contributions of all clients C actually make sense with regard to the intended application of the neural network. The example was already mentioned before that, due to a misunderstanding between client C and central entity Q, training examples are used that do not fit the intended application at all. In addition, it is also possible, for example, that individual clients C constantly use training examples of poor technical quality. For example, camera images may be incorrectly exposed and/or out of focus, meaning that the essence of them cannot be seen.

ermittelt werden. Anhand dieser Zeitentwicklung und/oder Statistik kann dann eine Drift des Verhaltens des neuronalen Netzwerks, und/oder eine Verschlechterung des Verhaltens des neuronalen Netzwerks bezüglich bisheriger Trainings-Beispiele x beim Weitertraining mit neuen Trainings-Beispielen x detektiert werden. So könnte beispielsweise ein inkrementelles Training des neuronalen Netzwerks mit immer neuen Batches von Trainings-Beispielen dazu führen, dass ein aus früheren Trainings-Beispielen gelerntes „Wissen“ wieder in „Vergessenheit“ gerät (sogenanntes „catastrophic forgetting“).For example, a time development and/or statistics about the reconstructed training examples ${\tilde{x}}_j^T$

be determined. Based on this time development and/or statistics, a drift in the behavior of the neural network and/or a deterioration in the behavior of the neural network with respect to previous training examples x can then be detected during further training with new training examples x. For example, incremental training of the neural network with ever new batches of training examples could lead to “knowledge” learned from previous training examples being “forgotten” again (so-called “catastrophic forgetting”).

Alternatively or in combination with this, a control intervention in the cooperation between the central entity Q and the clients C can be carried out. This control intervention can in particular have the aim, for example, of stopping or reversing a previously determined deterioration or drift. A control intervention can in particular include, for example, temporarily or permanently disregarding the gradients dL/dM _W supplied by at least one client C.

The method can in particular be implemented entirely or partially by computer. Therefore, the invention also relates to a computer program with machine-readable instructions which, when executed on one or more computers and/or compute instances, cause the computer(s) and/or compute instances to carry out the method described. In this sense, control devices for vehicles and embedded systems for technical devices that are also capable of executing machine-readable instructions are also considered computers. Examples of compute instances include virtual machines, containers, or serverless execution environments for executing machine-readable instructions in a cloud.

The invention also relates to a machine-readable data carrier and/or to a download product with the computer program. A download product is a digital product that can be transferred via a data network, i.e. downloadable by a user of the data network and which can be offered for sale in an online shop for immediate download, for example.

Furthermore, a computer can be equipped with the computer program, with the machine-readable data carrier or with the download product.

Further measures improving the invention are shown in more detail below together with the description of the preferred exemplary embodiments of the invention using figures.

Examples of embodiments

• 1 Ausführungsbeispiel des Verfahrens 100 zum Rekonstruieren von Trainings-Beispielen x;
• 2 Veranschaulichung der auf eine Optimierung von Komponenten P_j einer Partition zurückgeführten Rekonstruktion.

It shows:

• 1 Embodiment of the method 100 for reconstructing training examples x;
• 2 Illustration of the reconstruction resulting from an optimization of components P _j of a partition.

1 is a schematic flow diagram of an exemplary embodiment of the method 100 for reconstructing training examples x with which a given neural network 1 was trained to optimize a given cost function L.

In step 110, a quality function R is provided which, for a reconstructed training example x̃, measures the extent to which it belongs to an expected domain or distribution of the training examples x. According to block 111, this quality function R can be a trained discriminator of a Generative Adversarial Network, GAN. As explained previously, probabilistic models can also be used, for example.

In step 120, a size B of a batch of training examples x with which the neural network was trained is provided.

In step 130, a gradient dL/dM _W of the cost function L determined during this training is divided into a partition of B components P _j according to parameters M _W that characterize the behavior of the neural network 1. Here, according to block 131, in particular, for example, shares p _j · dL/dM _W with weights p _j and Σ _j p _j = 1 can be selected as components P _j of the partition.

rekonstruiert.In step 140, each component P _j of the gradient dL/dM _W is converted from the parameters M W,i using the functional dependence of the outputs y _i of neurons in the input layer of the neural network 1, which receives the training examples _x Neurons and the training examples x one training example ${\tilde{x}}_j^T$

reconstructed.

und additive Bias-Werte b_i sein, die dem Trainings-Beispiel x am i-ten Neuron in der Eingangsschicht des neuronalen Netzwerks 1 zugeschlagen werden. Gemäß Block 141 können dann aus der Komponente P_j des Gradienten dL/dM_W Gradienten dL/db_i der Kostenfunktion L nach dem Bias b_i und Gradienten $dL/d{w}_i^T$

der Kostenfunktion L nach den Gewichten $w_i^T$

ermittelt werden. Gemäß Block 142 kann dann aus diesen Gradienten dL/db_i und $dL/d{w}_i^T$

die gesuchte Rekonstruktion ${\tilde{x}}_j^T$

des Trainings-Beispiels ermittelt werden. Wie zuvor erläutert, sollte hierfür die Aktivierungsfunktion eine ReLU-Funktion sein, und auf die Eingangsschicht des neuronalen Netzwerks 1 sollte unmittelbar eine dichte Schicht folgen. Weiterhin muss das neuronale Netzwerk 1 (dL/db_i) ≠ 0 gewährleisten.The parameters of the neural network can in particular, for example, be multiplicative weights $w_i^T$

and additive bias values b _i , which are added to the training example x on the ith neuron in the input layer of the neural network 1. According to block 141, gradients dL/db _{i of} the cost function L according to the bias b _i and gradients can then be derived from the component P _j of the gradient dL/dM W $dL/d{w}_i^T$

the cost function L according to the weights $w_i^T$

be determined. According to block 142, dL/db _i and $dL/d{w}_i^T$

the reconstruction you are looking for ${\tilde{x}}_j^T$

of the training example can be determined. As explained previously, the activation function for this should be a ReLU function, and the input layer of the neural network 1 should be immediately followed by a dense layer. Furthermore, the neural network must ensure 1 (dL/db _i ) ≠ 0.

According to block 143, the reconstruction can be carried out by a central entity Q, which distributes the neural network 1 to a plurality of clients C for the purpose of federated training. This is then accompanied by the fact that, according to block 132, the gradient dL/dM _W is determined by a client C when training the neural network 1 on a batch with B training examples x and is aggregated over these B training examples x.

mit der Gütefunktion R bewertet.In step 150 the obtained reconstructions ${\tilde{x}}_j^T$

rated with the quality function R.

deren Bewertung durch die Gütefunktion R verbessert wird.In step 160, the partition into the components P _j is optimized to the goal of redistributing the gradient dL/dM _W of the cost function L and reconstructing new training examples ${\tilde{x}}_j^T$

whose evaluation is improved by the quality function R.

According to block 161, a gradient of the quality function R can be propagated back to changes in the weights p _j .

According to block 162, the weights p _j can be initialized with softmax values formed from logits of the neural network 1.

dem neuronalen Netzwerk 1 als Validierungsdaten zugeführt.In step 170 the reconstructed training examples ${\tilde{x}}_j^T$

supplied to the neural network 1 as validation data.

In step 180, the outputs 3 then supplied by the neural network 1 are compared with target outputs 3a.

In step 190, the result of this comparison is used to determine to what extent the neural network 1 generalizes sufficiently to unseen data. In the in 1 In the example shown, this is classified in binary terms.

If the neural network 1 generalizes sufficiently (truth value 1), the neural network 1 is supplied in step 200 with measurement data 2 that were recorded with at least one sensor.

In step 210, a control signal 210a is determined from the output 3 then supplied by the neural network 1.

In step 220, a vehicle 50, a driving assistance system 60, a system 70 for quality control, a system 80 for monitoring areas, and/or a system 90 for medical imaging, is controlled with the control signal 210a.

können alternativ oder in Kombination hierzu auch in anderer Weise genutzt werden. In Schritt 230 wird hierzu eine Zeitentwicklung und/oder Statistik 4 über die rekonstruierten Trainings-Beispiele ${\tilde{x}}_j^T$

ermittelt. Anhand dieser Zeitentwicklung und/oder Statistik 4 wird

• • in Schritt 240 eine Drift 5a des Verhaltens des neuronalen Netzwerks 1, und/oder eine Verschlechterung 5b des Verhaltens des neuronalen Netzwerks 1 bezüglich bisheriger Trainings-Beispiele x beim Weitertraining mit neuen Trainings-Beispielen x detektiert, und/oder
• • in Schritt 250 ein Steuereingriff 6 in die Zusammenarbeit der zentralen Entität Q mit den Clients C vorgenommen.

The reconstructed training examples ${\tilde{x}}_j^T$

can alternatively or in combination be used in other ways. In step 230, a time development and/or statistics 4 about the reconstructed training examples are created ${\tilde{x}}_j^T$

determined. Based on this time development and/or statistics 4

• • in step 240 a drift 5a of the behavior of the neural network 1, and/or a deterioration 5b of the behavior of the neural network 1 with respect to previous training examples x is detected during further training with new training examples x, and/or
• • in step 250 a control intervention 6 is made in the cooperation of the central entity Q with the clients C.

According to block 251, the control intervention 6 may include, for example, temporary or permanent to disregard or underweight the gradients dL/dM _W provided by at least one client C, for example by downscaling.

2 illustrates reconstruction in a federated learning application where a central entity Q distributes the neural network to a plurality of clients C. Each client C trains the neural network 1 on a locally available batch with B training examples x, determines the gradient dL/dM _W of the cost function L according to the parameters M _W and passes this gradient dL/dM _W on to the central entity Q.

rekonstruiert. Die rekonstruierten Trainings-Beispiele ${\tilde{x}}_j^T$

werden mit der Gütefunktion R bewertet. Die Gewichte p_j, mit denen die Komponenten P_j der Partition ermittelt wurden, werden variiert mit dem Ziel, die Bewertung $R\left({\tilde{x}}_j^T\right)$

durch die Gütefunktion R zu verbessern. Wenn dieser iterative Prozess bis zu einem beliebigen Abbruchkriterium fortgeführt wird, entstehen am Ende rekonstruierte Trainings-Beispiele ${\tilde{x}}_j^T,$

die zumindest ähnlich zu den ursprünglichen Trainings-Beispielen x sind und der Domäne oder Verteilung dieser Trainings-Beispiele x angehören.The central entity Q breaks down the gradient dL/dM _W into a partition of components P _j with j = 1, ..., B. Each component P _j becomes its own training example ${\tilde{x}}_j^T$

reconstructed. The reconstructed training examples ${\tilde{x}}_j^T$

are evaluated with the quality function R. The weights p _j , with which the components P _j of the partition were determined, are varied with the aim of the evaluation $R\left({\tilde{x}}_j^T\right)$

to be improved by the quality function R. If this iterative process is continued up to any termination criterion, reconstructed training examples are created at the end ${\tilde{x}}_j^T,$

which are at least similar to the original training examples x and belong to the domain or distribution of these training examples x.

Claims (16)

Method (100) for reconstructing training examples x, with which a given neural network (1) was trained to optimize a given cost function L, with the steps: • a quality function R is provided (110), which is for a reconstructed Training example x̃ measures the extent to which it belongs to an expected domain or distribution of the training examples x; • a size B of a batch of training examples x with which the neural network 1 was trained is provided (120); • a gradient dL/dM _W of the cost function L determined during this training according to parameters M _W that characterize the behavior of the neural network (1) is divided into a partition of B components P _j (130); • Each component P _j of the gradient dL/dM _W is calculated using the functional dependence of the outputs y _i of neurons in the input layer of the neural network (1), which receives the training examples x, on the parameters M _W,i of this Neurons and the training examples x one training example ${\tilde{x}}_j^T$

reconstructed (140); • the reconstructions thus obtained ${\tilde{x}}_j^T$

are evaluated with the quality function R (150); • the partition into the components P _j is optimized to the goal (160) of splitting the gradient dL/dM _W of the cost function L again and reconstructing new training examples ${\tilde{x}}_j^T$

whose evaluation is improved by the quality function R. Procedure (100) according to Claim 1 , where shares p _j · dL/dM _W with weights p _j and Σ _j P _j = 1 are chosen as components P _j of the partition (131). Procedure (100) according to Claim 2 , whereby a gradient of the quality function R is propagated back to changes in the weights p _j (161). Method (100) according to one of Claims 1 until 3 , where the weights p _j are initialized with softmax values formed from logits of the neural network (1) (162). Method (100) according to one of Claims 1 until 4 , where a neural network (1) is chosen that weights $w_i^T$

and bias values b _i as parameters M _W,i , where an i-th neuron • a training example x supplied to this neuron with weights $w_i^T$

multiplied, • a bias value b _i is added to the result in order to obtain an activation value of the neuron and • an output y _i is determined by applying a nonlinear activation function to this activation value. Procedure (100) according to Claim 5 , where • from the component P _j of the gradient dL/dM _W gradient dL/db _i of the cost function L according to the bias b _i and gradient $dL/d{w}_i^T$

the cost function L according to the weights $w_i^T$

can be determined (141), and • from these gradients dL/db _i and $dL/d{w}_i^T$

the reconstruction you are looking for ${\tilde{x}}_j^T$

of the training example is determined (142). Method (100) according to one of Claims 1 until 6 , where a trained discriminator of a Generative Adversarial Network, GAN, is chosen as the quality function R (111). Method (100) according to one of Claims 1 until 7 , whereby training examples x are selected that represent images and/or time series of measured values. Method (100) according to one of Claims 1 until 8th , where • the reconstructed training examples ${\tilde{x}}_j^T$

dem neural network (1) are supplied as validation data (170), • the outputs (3) then supplied by the neural network (1) are compared with target outputs (3a) (180) and • are determined based on the result of this comparison (190 ), to what extent the neural network (1) generalizes sufficiently to unseen data. Procedure (100) according to Claim 9 , whereby • in response to the fact that the neural network (1) generalizes sufficiently to unseen data, the neural network (1) is supplied with measurement data (2) (200), which were recorded with at least one sensor, • from which the neural Network (1) supplied output (3) a control signal (210a) is determined (210), and • a vehicle (50), a driving assistance system (60), a system (70) for quality control, a system (80) for monitoring Areas, and / or a system (90) for medical imaging, with which the control signal (210a) is controlled (220). Method (100) according to one of Claims 1 until 10 , where • the reconstruction is carried out by a central entity Q (143), which distributes the neural network (1) to a plurality of clients C for the purpose of federated training, and • the gradient dL/dM _W from a client C during training of the neural network (1) is determined on a batch with B training examples x and is aggregated over these B training examples x (132). Procedure (100) according to Claim 11 , where • a time development and/or statistics (4) about the reconstructed training examples ${\tilde{x}}_j^T$

is determined (230), and based on this time development and/or statistics (4) • a drift (5a) of the behavior of the neural network (1), and/or a deterioration (5b) of the behavior of the neural network (1) with respect to previous ones Training examples x are detected during further training with new training examples x (240), and/or • a control intervention (6) is carried out in the cooperation of the central entity Q with the clients C (250). Procedure (100) according to Claim 12 , whereby the control intervention (6) includes (251) temporarily or permanently disregarding or underweighting the gradients dL/dM _W supplied by at least one client C. Computer program containing machine-readable instructions that, when executed on one or more computers, cause the computer or computers to perform a method according to one of the Claims 1 until 13 to carry out. Machine-readable data carrier with the computer program Claim 14 . One or more computers with the computer program Claim 14 , and/or with the machine-readable data carrier Claim 15 .

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